Numerical Evidence for Many-Body Localization in Two and Three Dimensions.

Disorder and interactions can lead to the breakdown of statistical mechanics in certain quantum systems, a phenomenon known as many-body localization (MBL). Much of the phenomenology of MBL emerges from the existence of ℓ bits, a set of conserved quantities that are quasilocal and binary (i.e., possess only ±1 eigenvalues). While MBL and ℓ bits are known to exist in one-dimensional systems, their existence in dimensions greater than one is a key open question. To tackle this question, we develop an algorithm that can find approximate binary ℓ bits in arbitrary dimensions by adaptively generating a basis of operators in which to represent the ℓ bit. We use the algorithm to study four models: the one-, two-, and three-dimensional disordered Heisenberg models and the two-dimensional disordered hard-core Bose-Hubbard model. For all four of the models studied, our algorithm finds high-quality ℓ bits at large disorder strength and rapid qualitative changes in the distributions of ℓ bits in particular ranges of disorder strengths, suggesting the existence of MBL transitions. These transitions in the one-dimensional Heisenberg model and two-dimensional Bose-Hubbard model coincide well with past estimates of the critical disorder strengths in these models, which further validates the evidence of MBL phenomenology in the other two- and three-dimensional models we examine. In addition to finding MBL behavior in higher dimensions, our algorithm can be used to probe MBL in various geometries and dimensionality.

Polymorphism of Crystalline Molecular Donors for Solution-Processed Organic Photovoltaics.

Using ab initio calculations and classical molecular dynamics simulations coupled to complementary experimental characterization, four molecular semiconductors were investigated in vacuum, solution, and crystalline form. Independently, the molecules can be described as nearly isostructural, yet in crystalline form, two distinct crystal systems are observed with characteristic molecular geometries. The minor structural variations provide a platform to investigate the subtlety of simple substitutions, with particular focus on polymorphism and rotational isomerism. Resolved crystal structures offer an exact description of intermolecular ordering in the solid state. This enables evaluation of molecular binding energy in various crystallographic configurations to fully rationalize observed crystal packing on a basis of first-principle calculations of intermolecular interactions.